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With great potential in studying neuro-development, neuro-degeneration, and the aging process, longitudinal image data is gaining increasing interest and attention in the neuroimaging community. In this paper, we present a parametric nonlinear model to statistically study multivariate longitudinal data with asymptotic properties. We demonstrate our preliminary results in a combined study of two longitudinal neuroimaging data sets of early brain development to cover a wider time span and to gain a larger sample size. Such combined analysis of multiple longitudinal image data sets has not been conducted before and presents a challenge for traditional analysis methods. To our knowledge, this is the first multivariate nonlinear longitudinal analysis to study early brain development. Our methodology is generic in nature and can be applied to any longitudinal data with nonlinear growth patterns that can not easily be modeled by linear methods.